In this paper, a hybrid conjugate gradient algorithm with weighted preconditioner is proposed. The algorithm can efficiently solve the minimizing problem of general function deriving from finite element discretization of the p-Laplacian. The algorithm is efficient, and its convergence rate is meshindependent. Numerical experiments show that the hybrid conjugate gradient direction of the algorit...

Epileptic seizures correspond to episodes of increased rhythmicity of the normally chaotic activity in biological neural networks. We propose to use hybrid neural networks where artificial neural networks are used to control the biological neural networks by learning their different states. The learning is dramatically accelerated when using a conjugate gradient method in conjunction with the F...

A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is employed. However, for more challenging systems a substantial error can be present even after many iterations have been performed. The estimates obtained in this ...

Two new nonlinear spectral conjugate gradient methods for solving unconstrained optimization problems are proposed. One is based on the Hestenes and Stiefel (HS) method and the spectral conjugate gradient method. The other is based on a mixed spectral HS-CD conjugate gradient method, which combines the advantages of the spectral conjugate gradient method, the HS method, and the CD method. The d...